Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions
IGCSE Maths Trigonometric Graphs Questions and Answers
Trigonometric Graphs questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 2 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
Trigonometric Graphs 2: Tangent & Properties: The graph of y = tan x: period, asymptotes and symmetry.
Trigonometric Graphs worked examples
Worked example 1: Solving with the sine graph
Solve \(\sin x=0.5\) for \(0^\circ\le x\le360^\circ\).
Solution
\(\sin^{-1}0.5=30^\circ\).
The sine graph is symmetrical about \(90^\circ\), so the other solution is \(180-30=150^\circ\).
Answer: \(30^\circ,\ 150^\circ\)
Tip: Sketch the graph to see how many solutions there are.
Worked example 2: Solving tan x = k
Solve \(\tan x=-1.5\) for \(0^\circ\le x\le360^\circ\).
Solution
\(\tan^{-1}(-1.5)=-56.3^\circ\), outside the range.
tan has period \(180^\circ\): add 180 and 360.
\(x=123.7^\circ\) or \(303.7^\circ\).
Answer: \(123.7^\circ,\ 303.7^\circ\)
Tip: Solutions of tan x = k are always 180° apart.
Trigonometric Graphs exam-style questions
Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.
Question 1 · easy · 1 mark
Write down the period of the graph of \(y=\tan x\).
Show the answer and mark scheme
B1 180°
Answer: 180°
Question 2 · medium · 3 marks
Solve \(\tan x=2\) for \(0^\circ\le x\le360^\circ\). Give your answers to 1 decimal place.
Show the answer and mark scheme
M1 tan⁻¹ 2
A1 63.4°
B1 243.4° ft their first angle + 180
Answer: \(x=63.4^\circ,\ 243.4^\circ\)
Question 3 · hard · 2 marks
How many solutions does the equation \(\tan x=5\) have for \(-360^\circ\le x\le360^\circ\)? Give a reason.
Show the answer and mark scheme
M1 one solution found (78.7°) and period 180° used
A1 4
Answer: 4
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Which Edexcel IGCSE Maths papers test trigonometric graphs?
Either Higher tier paper, 1H or 2H, can test trigonometric graphs: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more trigonometric graphs questions?
In the IGCSE student hub: Unit 4 (Graphs & Functions) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.